Reshaping Teachers’ Mathematical Perceptions: Analysis of a Professional Development Task

As the focus of mathematics education moves from memorization toward reasoning and problem solving, professional development for in-service teachers must model these activities while simultaneously increasing participants’ mathematical knowledge. We examine a representative task from a mathematics professional development course that uses rational number operation as an opportunity for problem solving and modeling. Transcripts exemplify the growth teachers make in deeply understanding the content—division of fractions—while engaging in guided reinvention and classroom discourse. We propose 4 interconnected qualities of this task that allow participants to engage in and reflect on the process of guided reinvention: (1) authentic context with multiple solution methods, including visual; (2) cognitive dissonance; (3) deep engagement; and (4) impact on mathematical knowledge for teaching.